WEEK 10: PREDICTIVE CHECKS & FINAL PROJECT

Monday, March 13th

Today we will…

  • Questions from Lab/Challenge 9
  • Final Exam – What to Expect
  • Mini lecture on text:
    • Predictive Checks
  • Final Project work-time

Final Exam – What to Expect

Predictive Checks

Assess if the model would produce data similar to what was observed.

Danger

Predictive checks do not make predictions for new observations.

A little bit on Bayesian Statistics

Bayes!

Why do we care? An assessment of “subjective” choices!

Final Project – “subjective” choice

Requirements of a “good” regression model (LINE)

  • Linear Relationships
  • Indepdent Observations
  • Normality of Residuals
  • Constant / Equal Variance

Predictive Checks

  1. Fit a regression model to observed data.

  2. Obtain Predictions from the model and add random errors to the predictions.

  3. Compare simulated data to observed data.

  4. Iterate!

Fit Linear Regression lm

Simulated data: Obtain Predictions + Simulate Errors predict + rnorm

Regress Observed vs Simulated lm

Measure “similarity” – \(R^2\) proportion of variability explained

Similarity Measures

Could also use correlation (\(r\)), size of the sum of squared errors (\(SSE\)), or the estimate of \(\hat \sigma\) (\(RMSE\))

Iterate! map

Distribution of Simulated \(R^2\) geom_hist

To do…

  • Course Evaluation
    • Closes Friday, 3/17 at 11:59pm
  • Final Project Report
    • Due Sunday, 3/19 at 11:59pm

Wednesday, March 15th

Today we will…

  • Remaining Q & A
  • Course Evaluation
  • R Hex Cookies!
  • Final Project work-time

Q & A

Course Evaluation + Cookies!

To do…

  • Course Evaluation
    • Closes Friday, 3/17 at 11:59pm
  • Final Project Report
    • Due Sunday, 3/19 at 11:59pm
  • Final Exam
    • Section 70: Wednesday, 3/22 at 10:10am - 1:00pm
    • Section 71: Monday, 3/20 at 10:10am - 1:00pm